Heat flux effects on magnetic field dynamics in solid density plasmas traversed by relativistic electron beams

Relativistic electron beam propagation through solid density plasma is a rich area for magnetic field dynamics. It is well known that Ohmic heating of the background plasma caused by the beam significantly affects magnetic field generation, primarily through changes in the resistivity. In particular, temperature changes in the background plasma leads to the generation of a magnetic field that acts to deflect relativistic electrons from the beam axis. This 'beam hollowing' field could have disastrous implications for the fast ignitor scheme. In this paper, the effects of background heat flow on magnetic field generation are considered, first with a simple analytic investigation, and then with 1D Vlasov Fokker–Planck and classical transport simulations using a rigid beam for the fast electrons. It is shown that the thermal conduction of the background plasma acts to diffuse the temperature, reducing both the temperature gradients and the beam hollowing field. This gives rise to the re-emergence of a collimating magnetic field. The influence of the background heat flux is also investigated in the context of solids with imposed resistivity gradients, and is shown to significantly enhance the magnetic field present. More exotic transport effects, such as an enhanced Nernst velocity (due to non-local heat flux) and double peaked temperature profiles (due to distortion of the heating and heat-flow profiles by the magnetic field), are also reported

Social tipping points and Earth systems dynamics

Recently, Early Warning Signals (EWS) have been developed to predict tipping points in Earth Systems. This discussion highlights the potential to apply EWS to human social and economic systems, which may also undergo similar critical transitions. Social tipping points are particularly difficult to predict, however, and the current formulation of EWS, based on a physical system analogy, may be insufficient. As an alternative set of EWS for social systems, we join with other authors encouraging a focus on heterogeneity, connectivity through social networks and individual thresholds to change

International consensus statement on nomenclature and classification of the congenital bicuspid aortic valve and its aortopathy, for clinical, surgical, interventional and research purposes

This International Consensus Classification and Nomenclature for the congenital bicuspid aortic valve condition recognizes 3 types of bicuspid valves: 1. The fused type (right-left cusp fusion, right-non-coronary cusp fusion and left-non-coronary cusp fusion phenotypes); 2. The 2-sinus type (latero-lateral and antero-posterior phenotypes); and 3. The partial-fusion (forme fruste) type. The presence of raphe and the symmetry of the fused type phenotypes are critical aspects to describe. The International Consensus also recognizes 3 types of bicuspid valve-associated aortopathy: 1. The ascending phenotype; 2. The root phenotype; and 3. Extended phenotypes.Cardiolog

Dimensional analysis and dimensional reasoning

This chapter explores some of the ways physical dimensions, such as length, mass and time, impact on the work of scientists and engineers. Two main themes are considered: dimensional analysis, which involves deriving algebraic expressions to relate quantities based on their dimensions; and dimensional rea-soning, a more general and often more subtle approach to problem solving. The method of dimensional analysis is discussed both in terms of its practical applica-tion (including the derivation of physical formulae, the planning of experiments, and the investigation of self-similar systems and scale models) and its conceptual contribution. The connection between dimensions and the fundamental concept of orthogonality is also described. In addition to these important uses of dimensions, it is argued that dimensional reasoning (using dimensionless comparisons to sim-plify models, the application of dimensional homogeneity to check for algebraic consistency, and the ‘mapping-out’ of solutions in terms of parameter space) forms the implicit foundation of nearly all theoretical work and plays a central role in the way scientists and engineers think about problems and communicate ideas

On oscillatory convection with the Cattaneo-Christov hyperbolic heat-flow model

Adoption of the hyperbolic Cattaneo–Christov heat-flow model in place of the more usual parabolic Fourier law is shown to raise the possibility of oscillatory convection in the classic Bénard problem of a Boussinesq fluid heated from below. By comparing the critical Rayleigh numbers for stationary and oscillatory convection, Rc and RS respectively, oscillatory convection is found to represent the preferred form of instability whenever the Cattaneo number C exceeds a threshold value CT≥8/27π2≈0.03. In the case of free boundaries, analytical approaches permit direct treatment of the role played by the Prandtl number P1, which—in contrast to the classical stationary scenario—can impact on oscillatory modes significantly owing to the non-zero frequency of convection. Numerical investigation indicates that the behaviour found analytically for free boundaries applies in a qualitatively similar fashion for fixed boundaries, while the threshold Cattaneo number CT is computed as a function of P1∈[10−2,10+2] for both boundary regimes

Discontinuity waves as tipping points: Applications to biological & sociological systems

The `tipping point' phenomenon is discussed as a mathematical object, and related to the behaviour of non-linear discontinuity waves in the dynamics of topical sociological and biological problems. The theory of such waves is applied to two illustrative systems in particular: a crowd-continuum model of pedestrian (or traffic) flow; and an hyperbolic reaction-diffusion model for the spread of the hantavirus infection (a disease carried by rodents). In the former, we analyse propagating acceleration waves, demonstrating how blow-up of the wave amplitude might indicate formation of a `human-shock', that is, a `tipping point' transition between safe pedestrian flow, and a state of overcrowding. While in the latter, we examine how travelling waves (of both acceleration and shock type) can be used to describe the advance of a hantavirus infection-front. Results from our investigation of crowd models also apply to equivalent descriptions of traffic flow, a context in which acceleration wave blow-up can be interpreted as emergence of the `phantom congestion' phenomenon, and `stop-start' traffic motion obeys a form of wave propagation

Field Compressing Magnetothermal Instability in Laser Plasmas

The mechanism for a new instability in magnetized plasmas is presented and a dispersion relation derived. Unstable behavior is shown to result purely from transport processes—feedback between the Nernst effect and the Righi-Leduc heat-flow phenomena in particular—neither hydrodynamic motion nor density gradients are required. Calculations based on a recent nanosecond laser gas-jet experiment [ D. H. Froula et al. Phys. Rev. Lett. 98 135001 (2007)] predict growth of magnetic field and temperature perturbations with typical wavelengths of order 50  μm and characteristic growth times of ∼0.1  ns. The instability yields propagating magnetothermal waves whose direction depends on the magnitude of the Hall parameter

Super-Gaussian transport theory and the field-generating thermal instability in laser-plasmas

Inverse bremsstrahlung (IB) heating is known to distort the electron distribution function in laser–plasmas from a Gaussian towards a super-Gaussian, thereby modifying the equations of classical transport theory (Ridgers et al 2008 Phys. Plasmas 15 092311). Here we explore these modified equations, demonstrating that super-Gaussian effects both suppress traditional transport processes, while simultaneously introducing new effects, such as isothermal (anomalous Nernst) magnetic field advection up gradients in the electron number density ne, which we associate with a novel heat-flow qn∝∇ne. Suppression of classical phenomena is shown to be most pronounced in the limit of low Hall-parameter χ, in which case the Nernst effect is reduced by a factor of five, the ∇Te × ∇ne field generation mechanism by ~30% (where Te is the electron temperature), and the diffusive and Righi–Leduc heat-flows by ~80 and ~90% respectively. The new isothermal field advection phenomenon and associated density-gradient driven heat-flux qn are checked against kinetic simulation using the Vlasov–Fokker–Planck code impact, and interpreted in relation to the underlying super-Gaussian distribution through simplified kinetic analysis. Given such strong inhibition of transport at low χ, we consider the impact of IB on the seeding and evolution of magnetic fields (in otherwise un-magnetized conditions) by examining the well-known field-generating thermal instability in the light of super-Gaussian transport theory (Tidman and Shanny 1974 Phys. Fluids 12 1207). Estimates based on conditions in an inertial confinement fusion (ICF) hohlraum suggest that super-Gaussian effects can reduce the growth-rate of the instability by 80%. This result may be important for ICF experiments, since by increasing the strength of IB heating it would appear possible to inhibit the spontaneous generation of large magnetic fields

Compartmental modelling of social dynamics with generalised peer incidence

A generalised compartmental method for investigating the spread of socially determined behaviour is introduced, and cast in the specific context of societal smoking dynamics with multiple peer influence. We consider how new peer influence terms, acting in both the rate at which smokers abandon their habit, and the rate at which former smokers relapse, can affect the spread of smoking in populations of constant size. In particular, we develop a three-population model (comprising classes of potential, current, and former smokers) governed by multiple incidence transfer rates with linear frequency dependence. Both a deterministic system and its stochastic analogue are discussed: in the first we demonstrate that multiple peer influence not only modifies the number of steady-states and nature of their asymptotic stability, but also introduces a new kind of non-linear "tipping-point" dynamic; while in the second we use recently compiled smoking statistics from the Northeast of England to investigate the impact of systemic uncertainty on the potential for societal "tipping". The generality of our assumptions mean that the results presented here are likely to be relevant to other compartmental models, especially those concerned with the transmission of socially determined behaviours